Most varieties of mushrooms are cleaned and stored in the same fashion: Store on a plate or tray, lightly covered with cloth, or in an open paper bag. Don't wrap them too tightly or they'll spoil quickly.
Fresh mushrooms need only be quickly and carefully rinsed immediately prior to cooking. They are extremely absorbent and take on a great deal of water if soaked, thereby diluting their flavors.
Dried mushrooms need to be well-rinsed, then rehydrated by soaking them in liquid such as water, broth or wine. Make sure to drain them well, avoiding the grit at the bottom of the soaking liquid, and use the broth in a sauce or stock. Trim all stems and save for stock.